Artificial intelligence (AI) is expected to play a key role in 6G networks, including optimizing system management, operation, and evolution. This requires systematic lifecycle management of AI models, ensuring their impact on services and stakeholders is continuously monitored. While current 6G initiatives introduce AI, they often fall short in addressing end-to-end intelligence and crucial aspects like trust, transparency, privacy, and verifiability. Trustworthy AI is vital, especially for critical infrastructures like 6G. This article introduces the REASON approach for holistically addressing AI's native integration and trustworthiness in future 6G networks. The approach comprises AI orchestration (AIO) for model lifecycle management, cognition (COG) for performance evaluation and explanation, and AI monitoring (AIM) for tracking and feedback. Digital twin (DT) technology is leveraged to facilitate real-time monitoring and scenario testing, which are essential for AIO, COG, and AIM. We demonstrate this approach through an AI-enabled xAPP use case, leveraging a DT platform to validate, explain, and deploy trustworthy AI models.